the answer

An ice cube does melt much faster in tap water than in salt water. The reason has to do with different rates of conduction of heat from the surrounding water to the ice cube.

When an ordinary ice cube melts in a regular glass of water, you have to remember that cold water (like the water from the ice cube) is actually denser than warm water (like the surrounding water in the glass). This is because cold water molecules have less energy and are a tiny bit closer together than molecules in warmer water. So as the ice cube melts, the cold water coming from it sinks to the bottom of the glass and the warm water from the bottom comes up to take its place. The water in the glass is therefore constantly moving, warming the ice cube by something called 'convection currents.'

But salt water is much denser than tap water, warm or cold, because of the salt in it. So when you put a freshwater ice cube into a glass of salt water, the cold water coming from the melting ice cube doesn't sink at all. Instead, the dense salt water stays at the bottom of the glass and the cold less-dense fresh water floats on top. Without any convection currents to carry the cold water away from the ice cube, the ice cube sits in relatively cold water and melts much more slowly.